Related papers: The Ambiguous Class Number Formula Revisited

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

We improve the previuosly known bound for some vertex Folkman numbers.

In 1988, Gross proposed a conjectural congruence between Stickelberger elements and algebraic regulators, which is often referred to as the refined class number formula. In this paper, we prove this congruence.

We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…

In this paper we present a short and elementary proof for the error in Simpson's rule.

We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

In this note we provide a simple formula of general term of recurrent sequence.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.

We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.

In this paper, we give a class of reconstructible graphs.

In this note we prove an inequality involving primes and the product of consecutive primes.

We formulate a generalization of a `refined class number formula' of Darmon. Our conjecture deals with Stickelberger-type elements formed from generalized Stark units, and has two parts: the `order of vanishing' and the `leading term'.…

It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.

The note contains a short elementary proof of Cayley's formula for labeled trees.

A classical result of Dirichlet shows that certain elementary character sums compute class numbers of quadratic imaginary number fields. We obtain analogous relations between class numbers and a weighted character sum associated to a…